At 1.30 p.m., Shannon and Archie left Hotel B for Hotel C at average speeds of 72 km/h and 58 km/h respectively. Upon reaching Hotel C, Shannon rested for 20 minutes. She then headed back for Hotel B at an average speed of 72 km/h along the same route. Archie and Shannon met each other on their way at 6 p.m.

1. How much more distance had Shannon covered than Archie when they met on their way?
2. How far apart were Hotel B and Hotel C? Express your answer in mixed number.

(a)
Duration from 1.30 p.m. to 6 p.m. = 4 h 30 min = 4¹₂ h
Duration from 1.30 p.m. to 6 p.m. without 20 min rest = 4 h 10 min = 4¹₆ h

60 min = 1 h
30 min = ³⁰₆₀ = ¹₂ h
10 min = ¹⁰₆₀ = ¹₆ h


Distance covered by Shannon
= 72 x 4¹₆
= 72 x ²⁵₆ 
= 300 km

Distance covered by Archie
= 58 x 4¹₆
= 58 x ²⁵₆
= 261 km

Distance that Shannon covered more than Archie
= 300 - 261
= 39 km

(b)
Distance between Hotel B and Hotel C
= (300 + 261) ÷ 2
= 561 ÷ 2
= 280¹₂ km

Answer(s): (a) 39 km; (b) 280¹₂ km